Eggs washed in cold water

Ok, just a question. My daughter needed two dozen eggs for school today to make crepes. We dont wash our eggs when we store them, just rinse them before we use them. Well we've had a lot of rain so we've had some muddy eggs lately. Before I sent them to school I rinsed them all, using a new sponge to get them clean, dried them and sent her on her way. I just realized that I used cold water to rinse them. They will be cooked all the way, but now im worried. Should they be ok since they will be cooked or should I just go by her two dozen and drop them off to her on my way to work? Ahhhh.....

They will be fine I wash all 30 of my eggs from my 32 Golden Buff hens every day before I put them in refrigerator. When I boil or make breakfast I use same eggs no more washing. Been doing same way for about 5 years now. No problem, oh my kids use these eggs to